An ongoing review of politics and culture

John Broome, in his cover article for the most recent Scientific American, tries to help us think though how to compare current economic costs of emitting less carbon dioxide with the economic benefits such mitigation is projected to provide to future generations. In plain English, when somebody tells us that we should give up $X of economic consumption today in order to save ourselves $Y of global warming-driven losses in the future, how do we decide if this is a good deal, even if we accept X and Y?

There is a common-sense element to this. As we all know from everyday life, normally I would rather have a dollar today than the promise of a dollar a year from now. I “discount” the promise. Roughly speaking, the amount of cash I would be willing to take today in lieu of that promised dollar is termed its “present value,” and the percentage lower I am willing to accept today is called the “discount rate.”

In the global warming debate, however, we are discussing how to compare costs over at least the next several decades with benefits that are projected to obtain over the next several hundred years. When decisions are made on the timescale of centuries, discounting can have counterintuitively large effects: Consider that if the legendary sellers of Manhattan Island had put $28 in an account with a 4 percent real interest rate in 1626, they would have enough money in the bank today to buy back all of the land in Manhattan. Albert Einstein supposedly said that “the most powerful force in the universe is compound interest” — and this mathematical reality is central to the correct evaluation of plans to address the risk of climate change.

Broome provides a chart showing that a promise of a $1 trillion benefit 100 years from now has a present value of $247 billion if we use a 1.4% discount rate, and $2.5 billion if we use a discount rate of 6%. That is, the lower discount rate leads us to value this future benefit 100 times more than the higher discount rate.

I hope this makes it obvious why there is a fierce battle in the nerdier end of the global warming debate to control the discount rate assumption. Broome did not select his example discount rates arbitrarily. The “Stern Review,” produced by the British government last year, is cited frequently as demonstrating that the world should begin immediate, aggressive emissions abatement, and it used a 1.4% discount rate. William Nordhaus, a Yale professor widely considered to be the world’s leading expert on this kind of integrated environmental-economic assessment, advocated a 6% discount rate.

Broome poses the question, then, as what discount rate should we use? As I’ll explain, I think this is a poor question, and the far more useful question is the more direct one: would I trade the projected near-term costs of some specific proposed policy for the projected long-term benefits that it promises?

Here’s why.

If you ask me whether a given discount rate makes sense, I will immediately start to consider the decisions that it would imply under a wide variety of test cases. The rate that under a wide variety of relevant cases advocates the trade-offs between costs and benefits over time that strike me as correct (or fair or ethical or whatever) is the one I will support.

Consider the Stern Review assumption of a very low discount rate. To demonstrate just how unrealistic that assumption is, Nordhaus asks us to imagine a scenario in which global warming would lead to zero costs between now and the year 2200, at which point global economic growth would be permanently reduced by 0.1 percent — in other words, that economic output starting in 2200 would be 99.9 percent of what it would have been had there been no global warming. Under this scenario, how much should we be willing to pay today as a lump sum to avoid this cost? Using the assumptions of the Stern Review, Nordhaus points out, we would pay about $30 trillion, which is more than half of the world’s entire annual economic output. Thanks, but no thanks.

Interestingly, in his pointers to further reading, Broome completely loads the dice on this, the central issue of his article. Last May, Nordhaus wrote a massive, and massively influential, reply to the Stern Review. Stern and Nordhaus had a famous debate on this exact question at Yale. Where does Broome point his readers?: to Nordhaus’s 15 year-old paper on the general question of economic analysis of warming. Broome is obviously current on the debate, as he also points readers to Weitzman’s much more sophisticated attempt to raise the present value of future costs by adopting a non-standard utility functional form.

But the whole debate about rates (and in Weitzman’s case, functional forms) strikes me as formalism run amok. When it comes time to consider whether I support a specific policy, I would want to see the data on projected costs and benefits by time period in order to come to a decision, rather than rely on the single-number estimate of net benefits created by any discounting (or, more generally, utility) function. The primary practical use for these discounting / utility functions in global warming analysis is to have a function that allows integrated environment-economics models to search a wide space of possible policies automatically with a commonly-applied set of explicit assumptions without requiring human intervention to consider each model run. When it comes time to look at the policies that the model says are best, I would always want to see the actual data by time period for a variety of “good” scenarios to determine what policy I think makes sense.

Think of these models as being like a Google search. With infinite time and patience, I could review every document on the Web, but I have only finite time. The Google PageRank algorithm imperfectly, but usefully, narrows down the number of documents I need to review; usually, however, I don’t use the “I Feel Lucky” button, and certainly would not in a case where my life depended on it.

Why, in fact, should I believe that there is any discounting function relevant to global warming that exists in closed form? I have a set of preferences for comparing current to future scenarios of projected costs vs. benefits. Much of the knowledge that informs this set of preferences is tacit and/or contingent on elements of the scenarios that I didn’t list comprehensively in advance, but react to as I am presented with specific scenarios. This is of particular practical importance in a case like global warming which operates across a scope – centuries of time across the globe – in which many of the embedded assumptions that I use when making discounting assumptions in day-to-day life will likely be violated. If an economist can’t find a function that encompasses these, I’m not necessarily irrational; the economist just can’t model my beliefs in a way that he finds convenient. The discounting function is merely a heuristic, not some straightjacket that I have agreed to be bound by just because I haven’t disputed its assumptions.

When we consider this in these common-sense terms, and remember that the IPCC’s expected case is that a much richer world will lose about 3% of its income more than a century from now, you have to do some pretty fancy footwork with discount rates to get me super-excited about accepting big costs today to avoid this.

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Jim,

Here’s a good (meta-ethical, psychological, political) bet: economic analysis (however it falls out) will not persuade the American people to incur massive economic costs to stop (ameliorate) global warming; in fact, insofar as the conversation remains economic in flavor, the more aggressive global-warming policy advocates have already lost.

There’s one way the aggressive policy advocates win the political debate (and everybody knows it):

1) Moralize the issue (i.e., appeal to our moral intuitions and the sub-rational faculties which underpin them) — hence all the hoopla about justice and duty. This is what the Europeans have done, and what our Christian-afterimage moral universalists want to happen in America; however, this kind of emo-Singerian broadening of the circle is highly unlikely to happen in a place like China, who’s a necessary partner but unlikely fellow-traveler: a reality which makes the moralizing route, rather than a path to a fix, something akin to the problem-perpetuating self-congratulation of old-school noblesse oblige and new-school foreign aid: it won’t solve the problem, may not even dampen it, may even enable and amplify other, equally serious problems…but boy will it feel good.

One last note: I’m not so sure it’s a good thing, either as precedent or outcome, to unify billions of people by appealing to sub-rational, inscrutable, intractable faculties, unless you’re sure to get all of the big groupings on board. Otherwise, you’re just creating yet another emotionally charged, nigh ineradicable distinction between the “enlightened” in-group (those who have embraced the moral imperative) and the recalcitrant out-group (those who maintain a smaller, tighter circle, and serve their foreign policy cold), and, given the amount of money involved, a new first and second estate. In fact, it makes me slightly uncomfortable: Gaia the religion may create good externalities in the long-run, but it’s still a religion; it’s still dangerous when harnessed, unsympathetic when wielded, with adherents who prove the aphorism that you can’t argue men out of opinions they were never argued into. Not good, that.

I know you placed it elsewhere, but could you re-link through to the IPCC’s expectation of a 3% GDP loss? Depending on how they model that there is probably at least an implicit discounting going on through the future (if they model investments/consumption).

These are really good posts – but I’d like to see you tie them together. Doesn’t using lose as a percent of GDP (which you conclude with, and have used elsewhere) bias the argument in favor of Western, Europoean nations? (I’m speaking with my Global Citizen Hat on, as opposed to my USA Flag Hat, for a second.) The USA/EU has 56% of GDP – Kenya = .05%. If Global Warming caused Kenya to get wiped from the map in a water war (dramatic example, but let’s run with it) – it may actually not even be a distinguishable event on a GDP chart. (That’s why I’m curious as to the original study, how they handle this asymmetry of lose.)

Also – you are right. Discount rates are, for all intents, useless as a financial modeling tool after 5 years. Certainly after 20. Also it is tough to “discount” someone’s life, since it doesn’t have an opportunity cost (as opposed to a dollar) – one can’t fold potential wars in Africa into a discount rate outside of GDP loss.

Thanks for the comment. And I had the exact smae reaction as your brother Ben A.

Mike:

Here is the reference: http://www.ipcc.ch/pdf/assessment-report/ar4/wg2/ar4-wg2-spm.pdf

This is the IPCC 4AR WG2 SPM. Go to page 17.

In efect, it assumes (falsely) that everything that matters can be measured by money. You raise one great example of this. It is obviously a limitation, but remember that (i) if you really want to help people in Kenya (and of course, this begs the question – who are the “we” that should be the basis for policy), you can do a whole lot with money and the things it buys, so if your policy to help them with respect to AGW ends up impovershing them and you, in the end, everybody is worse off, and (ii) if you retard developed world economic growth, you will retard the growth of these countries, however you slice it, so you’re going to make them much more vulnerable to AGW plus every other bad thing that could happen to them and continue to make them more dependent on the West.

In one sense, Jim, I agree with your Kenya argument: if I had $50 to $100 billion a year to spend in any way I wished, I would devote almost all of it to public-heath interventions in developing countries.

But frankly, the only reason this is still a possibility is that the public doesn’t subscribe to the kinds of utilitarian assumptions that you and I take for granted. Yes, if I could spend money either on treating malaria or on mitigating climate change, I would spend it on treating malaria, but the very fact that we aren’t fully treating malaria (yet spend billions in foreign aid payoffs to countries like Israel and Egypt) indicates that public policy doesn’t operate according to a fully utilitarian framework. I happen to think that this is a bad thing, but I still have to work within the system to push for the enactment of policies I think are optimal.

I think that the public is generally more willing to spend for mitigation of harm we created (i.e. “our wildly disproportionate greenhouse gas arguments are hurting poor countries, and that matters”) than humanitarian aid for harms we had nothing to do with.

“We could transfer wealth directly to Kenya” is not an appropriate way to rebut the fact that aggregate-GDP accounting will functionally ignore Kenya, when its implicit premise also suggests that we should be giving lots of money to Kenya right now.

Note that “money isn’t everything” is, if anything, a even more powerful retort to the idea of exclusively using market interest rates to discount future damages. As a first approximation, it’s sensible to assume that there are two broad categories of harm from climate change: (1) harm that lowers utility by lowering consumption, and (2) harm that lowers utility in some other way. While the first probably should be discounted at market rates, the second certainly should not. In fact, a positive rate of pure time preference is the only way to keep the harms from (2) from exploding to infinity; this means that present value damages from (2) may be multiple orders of magnitude higher than those from (1), in a way that’s heavily dependent on what rate of time preference we choose.

Moral of the story: Even if (2) is a tiny part of current-value damages, it still has the potential to be a dominant part of the present-value impact on utility, and therefore a pivotal consideration in our analysis of climate change.

Yes, I introduced that because I was trying to make the argument that runs contrary to mine in the strongest possible light.

The point of this post was quite narrow: to describe why I think the whole debate about discount rates, as opposed to discounting, is sterile and misguided. There is not really much point in trying to establish an a priori discount rate or function, when I can simply look at the vector of projected costs and benefits by time period that various policies are expected to produce and rank-order them myslef, rather than using some function form to convert each vector to a scalar then rank-order them for me.

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